Problem: Multiply the following complex numbers: $({5i}) \cdot ({4+4i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5i}) \cdot ({4+4i}) = $ $ ({0} \cdot {4}) + ({0} \cdot {4}i) + ({5}i \cdot {4}) + ({5}i \cdot {4}i) $ Then simplify the terms: $ (0) + (0i) + (20i) + (20 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 20)i + 20i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 20)i - 20 $ The result is simplified: $ (0 - 20) + (20i) = -20+20i $